﻿const int N = 101;
class Solution {
public:
    vector<vector<int>> matrixBlockSum(vector<vector<int>>& mat, int k) {
        int m = mat.size(), n = mat[0].size();
        long long dp[N][N] = { 0 };
        for (int i = 1; i <= m; i++)
        {
            for (int j = 1; j <= n; j++)
            {
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1] + mat[i - 1][j - 1] - dp[i - 1][j - 1];
            }
        }

        vector<vector<int>> ans;
        for (int i = 0; i < m; i++)
        {
            vector<int> ele;
            for (int j = 0; j < n; j++)
            {
                int x1 = max(0, i - k) + 1;
                int x2 = min(i + k, m - 1) + 1;
                int y1 = max(0, j - k) + 1;
                int y2 = min(j + k, n - 1) + 1;
                ele.push_back(dp[x2][y2] - dp[x2][y1 - 1] - dp[x1 - 1][y2] + dp[x1 - 1][y1 - 1]);
            }
            ans.push_back(ele);
        }
        return ans;

    }
};